Enhancing in vivo cell and tissue targeting by modulation of polymer nanoparticles and macrophage decoys

The in vivo efficacy of polymeric nanoparticles (NPs) is dependent on their pharmacokinetics, including time in circulation and tissue tropism. Here we explore the structure-function relationships guiding physiological fate of a library of poly(amine-co-ester) (PACE) NPs with different compositions and surface properties. We find that circulation half-life as well as tissue and cell-type tropism is dependent on polymer chemistry, vehicle characteristics, dosing, and strategic co-administration of distribution modifiers, suggesting that physiological fate can be optimized by adjusting these parameters. Our high-throughput quantitative microscopy-based platform to measure the concentration of nanomedicines in the blood combined with detailed biodistribution assessments and pharmacokinetic modeling provides valuable insight into the dynamic in vivo behavior of these polymer NPs. Our results suggest that PACE NPs—and perhaps other NPs—can be designed with tunable properties to achieve desired tissue tropism for the in vivo delivery of nucleic acid therapeutics. These findings can guide the rational design of more effective nucleic acid delivery vehicles for in vivo applications.


Supplementary Figure 5. Gating Strategy for Homogenized Organs Analyzed by Flow
Cytometry.Cells were first selected from total events using a Hoechst 33342 stain to remove non-nucleated cells and fragments.Nucleated cells were then selected for single cells using a forward scatter height by forward scatter area selection.From there, bulk cells were evaluated for NP signal using the fluorescent dye contained within the NP (DiD-APC channel) and compared to cells from animals without NPs.Bulk cells were also sorted into specific cell populations, using fluorescent antibody markers, and gated based on unstained cells from the same population.These specific cell types were then evaluated for NP signal using the fluorescent dye contained within the NP (DiD-APC channel), and compared to cells from animals without NPs.

PBPK Model Parameterization
A constant rate of administration was assumed to last for the first 20 seconds of the simulation, with a dose rate calibrated to ensure the correct dose was administered.We initially set elimination constants Kurine = Kbile = 0 and verified that the administered dose (0.5 mg of PACE-PEG NPs, as in experiments in Figure 1) was conserved.We then assumed that Kurine = 0, and PAKidney = 0, based on previous experiments administering similarly sized polymeric NPs to ex vivo perfused human kidneys 7 .In these experiments, practically no NPs were excreted in the urine or diffused into the tubular or interstitial spaces.These experiments showed a far greater NP uptake in glomeruli than peritubular capillaries, which motivated our assumption that all NP uptake in the mouse kidneys in our study (an almost negligible amount, as shown in figure 1) is exclusively due to mesangial cell uptake of NPs in the glomeruli.Our second assumption was that the brain vascular permeability (denoted PABrain) was the same as the vascular permeability of the 'body' compartment.Mouse brain uptake of PACE NPs is practically negligible 8 , such that it was not required to quantify the NP concentration in brain tissue or include a detailed description of NP distribution in the brain compartment in our model.Lastly, we assumed that P was the same across gold and PACE-PEG NPs for all organs, and that the heart and bone marrow had the same P as the non-liver organs.
As stated previously, the model used in our study was originally developed using biodistribution data from PEGylated gold NPs in mice.To fit the model to our PACE NP data, we reparameterized the model by modifying the gold NP model's parameter values using Monte Carlo Importance Sampling (MCIS) 9 .MCIS involves running serial (10 4 ) simulations with the model, sampling parameter values from prescribed probability distributions, and updating the parameter distributions based on how well the simulation results fit the data.At the end of MCIS, parameters are represented as probability distributions, such that subsequent model simulations can be generated by sampling these parameter distributions to generate model results that are also probabilistic in nature.As such, the model not only provides a predicted value of NP concentration in the blood and tissue compartments, but also provides the probability that the model result lies within any specified interval.Beyond the utility of modeling PACE NP pharmacokinetics probabilistically, MCIS allows for the uncertainty of the experimental data to be encapsulated within the model, which can be used to avoid erroneous predictions that are not properly backed by the experimental data.
We parameterized the model with MCIS using a three-step procedure.Firstly, we used MCIS to rescale the parameters used to model PEGylated gold NPs by probabilistically sampling from uniform distributions to determine the order of magnitude difference required to match the model to our PACE biodistribution data.Once we rescaled the parameters, we then performed another round of MCIS, sampling from tighter uniform distributions to finetune the parameter distributions.Lastly, once the parameters were of the proper scale, we performed a third round of MCIS sampling from normal distributions.With each step, the model result was compared with experimental data in order to determine how best to rescale and ultimately estimate the parameter distributions.The data used to parameterize the model included the PACE-PEG NP concentration in the blood at 0.03, 1, 8 and 48 hours, and the relative NP concentration in each non-liver organ at 3 and 48 hours (excluding the 'body' and brain compartments), normalized to the liver (endpoint biodistribution data).
Biodistribution data was measured by quantifying NP fluorescence, which does not translate directly to the model-predicted mass of NPs in each organ.To compare the model results to the experimental data, we had to normalize the experimental data; the flow cytometry-based MFI for each organ (Figure 2f) was multiplied by that organ's cell number (Supplementary Table 2) and divided by the corresponding value (the product of MFI and cell number) of the liver: For the subscript i pertaining to each of the five non-liver organs.This resulted in five ratios Ri Liver of fluorescence intensity corresponding to the five non-liver organs that were evaluated in our experiments.The experimental data Ri Liver was calculated for each organ in each mouse, such that Ri Liver is distributed as a Gaussian with mean and standard deviation.The model results were compared to these experimental values by dividing the model-predicted sum of the mass of NPs in non-vascular sub-compartments in each organ by the sum of the NP mass in the non-vascular sub-compartments of the liver: We assume that the mass of NPs in the vascular space of each organ is negligible, after a cardiac perfusion was used to clear the mouse vasculature of unbound NPs.Thus, the vascular NP mass is not used in comparing the model result to the experimental data.For each model simulation, a value of ri Liver was calculated for each of the five non-liver organs.If the simulation ri Liver lay within the 99% confidence interval of the experimental data (Ri Liver ) for that organ, then that condition was assumed to be met (five possible conditions, at 3 and 48 hours for a total of ten conditions).
To fit the model to the 15 conditions (10 biodistribution and 5 blood concentration), we estimated values for 15 parameters: Kmax and K50 for each of the phagocytic organs (lungs, kidneys, liver and spleen), the Hill coefficient nH, assumed equal for all phagocytic organs, Kbile, and PA for the non-liver organs, excluding the kidney and including the 'body' compartment.We estimated these parameter values (subscript PACE) by scaling the parameter values associated with PEGylated gold NPs (subscript Au): ( ;!:$ ) /012 = ( ;!:$ ) 03 × 10 3 #$ (7) ( => ) "36+8,/012 = ( => ) "36+8,03 × 10 The probabilistic variable uij is uniformly distributed from -i to j, and is rounded to the nearest whole number: With each MCIS iteration, uij was sampled 15 times, one for each parameter.We refer to the above relations, collectively, as a 'sampling protocol.'The distribution uij was rounded so as to avoid redundancies in the parameter sets, so that the widest range of parameter combinations would be generated over the course of the serial simulations.The choice of ij was based on the bounds on each parameter used to model PEGylated gold NPs; for example, PA values for gold NPs (including 13nm and 100nm diameter NPs) were at most one order of magnitude larger or 5 orders of magnitude smaller than the values used to model the 100nm diameter gold NPs.The one exception are the K50 values for the phagocytic organs, which were only on the order of tens of hours in the source material.We opted to include the possibility that K50 is on the order of minutes or hundreds of hours.
As suggested by equations 1-6, The 15 parameters estimated above do not constitute the full set of parameters required to run the model.The phagocytic release constants Krel for all phagocytic organs and PALiver comprise eight additional parameters that needed to be estimated.However, importantly, these parameters can be estimated via correlation with the parameters already estimated above.These correlations follow directly from the steady-state conditions (subscript 'ss') of equations 2-6 (represented, respectively, as equations 7-11): ( %$: ) 88 =  %$: ( )*(+, ) 88 Where equation 9 is based on equation 4, with t ® ¥.Although we do not have the data to support predictions of the steady-state mass of NPs in any of the model compartments, we can assume that they are finite and nonzero.Indeed, it is possible that the steady-state values are zero, as the PACE-PEG NPs are eliminated from the mouse over time.This is why we use equations 7-11 to draw correlations between the parameters in a probabilistic manner, not to assume that we know the deterministic relationship between them.From equations 7-11, the following correlations emerge: For C a positive, unknown constant.Lastly, we may estimate Kmax for the non-liver phagocytic organs by assuming that: The above correlations translate to the following parameter sampling protocols in MCIS: ( %$: ) "!#$%,/012 = ( -(& ) "!#$%,/012 × 10 Note that, unlike the parameter sampling protocol for the parameters estimated by rescaling the gold NP parameters, these parameters are dependent on those 15 parameters initially estimated above (subscript PACE on both sides of each equivalence).Because we cannot ascertain the deterministic relationship between these 'correlated' parameters and the 'estimated' parameters with which they are correlated, we chose i=3 and j=3, to reduce any potential bias in estimating these parameters.The exception to this rule is (Krel)Liver, which we assume to be equal in order to or less than (Kmax)Liver, as this would be required to accumulate NPs in the liver to the point where the ratio of NPs accumulated in the non-liver organs and the liver could possibly be as low as seen experimentally.
The model was run 10 4 times, sampling from uij to produce 10 4 parameter sets (including the 15 parameters that were estimated by rescaling the gold NP parameters, and the 5 parameters estimated as multiples of the first 15).Each parameter set was used to generate a model time course of NP concentration in the blood and was used to compute endpoint biodistribution for each organ, normalized to the liver.The simulation runs that produced results that lay within the 99% confidence interval of the observed data were identified and the corresponding parameter sets were used to estimate the scaling factors required to generate the biodistribution results seen experimentally.These scaling factors were estimated by averaging the scales (the values of uij) across the simulation runs whose results were consistent with the data (lying within the 99% confidence interval).If the average of uij across these 'successful' simulation runs is denoted u_avg, we denote these constant scaling factors as su = 10 u_avg , recognizing that each of the twenty estimated parameters have their own unique scaling factor, numbered 1-20.
In the second MCIS step, we performed another 10 4 simulation runs, this time sampling from a continuous (unrounded) uniform distribution, vi:

Supplementary Figure 1 .
Time course of PACE-PEG NP biodistribution.(a) IVIS analysis of PACE-PEG NP uptake in various organs (heart, lungs, liver, spleen, kidneys, and bone) over time (0.5 mg dose per animal, 3 hours: orange, 6 hours: peach, 24 hours: purple, 48 hours: teal).Endpoint analysis of (b) whole organ fluorescence quantification of PACE-PEG NP uptake in various organs (n = 3 mice per group per organ; error bars represent standard deviation (SD)).End-point analyses of (c) %NP+ cells and (d) mean fluorescence intensity (MFI) in arbitrary units (arb.units) in homogenized organs by flow cytometry (n = 3 mice per group per organ; error bars represent SD).End-point analysis of (e) %NP+ cells and (f) MFI in homogenized liver populations (bulk, F4/80 + , and CD31 + ) by flow cytometry (n = 3 mice per group per population; error bars represent SD).End-point analyses of (g) %NP+ cells and (h) MFI in homogenized lung populations (bulk, CD45 + , and EpCAM + ) by flow cytometry (n = 3 mice per group per population; error bars represent SD).Supplementary Figure 2. PACE and PACE-PEG NP biodistribution in the F508del CF mouse model.(a) Schematic of the F508del CF mouse model illustrating the CF-associated 3 bp deletion in the CFTR gene.(b) Representative end-point IVIS analysis of PACE NP (blue) and PACE-PEG NP (purple) uptake in various organs (heart, lungs, pancreas, liver, spleen, kidneys, bone, and gastrointestinal (GI) tract)).End-point analyses of (c) whole organ fluorescence quantification of PACE and PACE-PEG NP uptake in various organs (n = 3 mice per group per organ; error bars represent standard error of the mean (SEM)), (d) %NP+ cells in homogenized organs by flow cytometry (n = 3 mice per group per organ; error bars represent SEM).Supplementary Figure 3. PBPK model validation.Experimental results of PACE NPs in the organs are compared to model results at the time points for which the data was not used to parameterize the PBPK model of PACE-PEG biodistribution in mice, shown as the organ NP mass (relative to the liver) at 6 and 24 hours post administration.(a) Mean values of the model (blue) and data (pink) are shown in blue and pink, respectively, with error bars to indicate standard deviations (model: n = 100 simulations per group per organ; data: n = 3 mice per group per organ).(b,c) The Z value caluclated based on the model and the data for the blood (b) and the corresponding model error quantified as the relative value of the model mean as compared to the data mean for the blood (c).These metrics are also shown for the organs at 6 hours post administration (d,e) and and 24 hours post administration (f,g).(h) Actual and model-predicted PACE-PEG NP blood concentration at all time points for all doses are compared, with calculated R 2 and root mean squared error (RMSE).(i) Organ mass of NPs normalized to the liver at all time points (3, 6, 24 and 48 hours post-administration) are compared, with calculated R 2 and RMSE.Supplementary Figure 4. Liver occupation by liposomes and intralipid.Representative epifluorescence liver images from three independent experiments of (a) untreated control and (b) DiI-loaded liposome-treated animals 24 hours post-IV administration.Nuclei are shown in blue, F4/80 + macrophages are shown in green, and DiI liposomes are shown in red.Scale bars, 100 µm.Representative liver histology images from three independent experiments with oil red "O" staining (red) of (c) untreated control and (d) intralipid-treated animals 24 hours post-IV administration.Arrows indicate lipid staining.Scale bars, 100 µm.

Supplementary Table 2. Physiological parameters used in mathematically modeling PACE NP pharmacokinetics.
*In lieu of a definitive value of vascularization of the heart, we assume it is the same as the kidney.Supplementary

Table 3 :
1arameters of the mathematical model.Parameters are presented in terms of their mean and standard deviation (SD).The coefficient of variation (CV) and normalized sensitivity coefficient (NSC) are presented for each parameter.Gray boxes include 'not applicable' (N/A) and CVs corresponding to parameters that were assumed correlated to estimated parameters.Blue boxes indicate significant CV and/or NSCs.'PEG/Au' refers to the value of that parameter corresponding to the source material, in which PEGylated gold NPs were modeled.1 3 #" (10) ( => ) 4!56$78,/012 = ( => ) 4!56$78,03 × 10 3 #"